Learn OpenGL. Lesson 6.3 - IBL. Diffuse irradiation

Lighting based on the image or * IBL 3r31207. (3-3331206. Image Based Lighting 3-3331207.) - is a category of lighting methods based not on analytical light sources (discussed in 3-331250. The previous lesson 3r-31297.), But considering the whole environment of the illuminated objects as one continuous light source. In general, the technical basis of such methods lies in processing a cubic environment map (prepared in the real world or created on the basis of a three-dimensional scene) so that the data stored in the map can be directly used in lighting calculations: virtually every texel of a cubic map is considered as a source of light. . In general, this allows you to capture the effect of global illumination in the scene, which is an important component that conveys the overall “tone” of the current scene and helps the illuminated objects to be better “embedded” in it. 3r3r1292. 3r? 31303. 3r3r1292. 3r? 31303. Since IBL algorithms take into account lighting from some kind of “global” environment, their result is considered to be a more accurate imitation of background lighting or even a very rough approximation of global lighting. This aspect makes IBL methods interesting in terms of inclusion in the PBR model, since the inclusion of ambient lighting in the lighting model allows objects to look much more physically correct. 3r3r1292. 3r? 31303. 3r3r1292. 3r? 31303. Creating a window 3r31297. 3r31287. 3r? 31303. 3r31284.Hello Window 3r31287. 3r? 31303. 3r31284. Hello Triangle 3r31287. 3r? 31303. 3r31284. Shaders 3r31287. 3r? 31303. 3r31284. Textures 3r31287. 3r? 31303. 3r31284. Transformation 3r31287. 3r? 31303. 3r31284. Coordinate systems 3r31297. 3r31287. 3r? 31303. 3r31284.Camera 3r31297. 3r31287. 3r? 31303.3r3r1292. 3r? 31303. Part 2. Basic lighting 3r31292. 3r? 31303. 3r3r1292. 3r? 31303. 3r? 31303. 3r31284. 3r388. Colors 3r31287. 3r? 31303. 3r31284. 3r33939. Lighting Basics 3r31297. 3r31287. 3r? 31303. 3r31284. 3r3398. Materials 3r31297. 3r31287. 3r? 31303. 3r31284. Texture maps 3r31297. 3r31287. 3r? 31303. 3r31284. 3r3108. Light Sources 3r31297. 3r31287. 3r? 31303. 3r31284. 3r3113. Multiple light sources 3r31297. 3r31287. 3r? 31303.3r3r1292. 3r? 31303. Part 3. Downloading 3D models 3r? 31303. 3r3r1292. 3r? 31303. 3r? 31303. 3r31284. 3r33132. Assimp library 3r31287. 3r? 31303. 3r31284. 3r33132. Mesh mesh class is3r31287. 3r? 31303. 3r31284. Class of the 3D model 3r31287. 3r? 31303.3r3r1292. 3r? 31303. Part 4. Advanced OpenGL features 3r? 31303. 3r3r1292. 3r? 31303. 3r? 31303. 3r31284. 3r3151. Depth test 3r31297. 3r31287. 3r? 31303. 3r31284. Stencil test 3r31297. 3r31287. 3r? 31303. 3r31284. 3r3161. Mixing colors 3r31297. 3r31287. 3r? 31303. 3r31284. 3r3r1616. Trimming faces 3r31287. 3r? 31303. 3r31284. 3r3171. Framebuffer3r31287. 3r? 31303. 3r31284. 3r3176. Cube maps 3r31297. 3r31287. 3r? 31303. 3r31284. 3r3181. Advanced work with data3r31287. 3r? 31303. 3r31284. 3r3186. Advanced GLSL3r31287. 3r? 31303. 3r31284. 3r3191. Geometric shader3r31287. 3r? 31303. 3r31284. 3r3196. Instancing3r31287. 3r? 31303. 3r31284. Smoothing 3r31297. 3r31287. 3r? 31303.3r3r1292. 3r? 31303. Part 5. Advanced lighting 3r31292. 3r? 31303. 3r3r1292. 3r? 31303. 3r? 31303. 3r31284.Advanced lighting. Model Blinna-Phong. 3r31297. 3r31287. 3r? 31303. 3r31284.Gamma Correction 3r31287. 3r? 31303. 3r31284. Shadow maps 3r31297. 3r31287. 3r? 31303. 3r31284.Omnidirectional shadow maps 3r31297. 3r31287. 3r? 31303. 3r31284.Normal Mapping 3r31297. 3r31287. 3r? 31303. 3r31284.Parallax Mapping 3r31287. 3r? 31303. 3r31284. HDR 3r31287. 3r? 31303. 3r31284. Bloom 3r31297. 3r31287. 3r? 31303. 3r31284.Pending rendering 3r31287. 3r? 31303. 3r31284. SSAO 3r31297. 3r31287. 3r? 31303.3r3r1292. 3r? 31303. Part 6. PBR 3r? 31303. 3r3r1292. 3r? 31303. 3r? 31303. 3r31284.Theory 3r31287. 3r? 31303. 3r31284. Analytical light sources 3r31287. 3r? 31303. 3r31284. 3r31294. IBL. Diffuse irradiation. 3r31295. 3r31287. 3r? 31303.3r3r1292. 3r? 31303. 3r? 31304. 3r? 31304. 3r3r1292. 3r? 31303. To incorporate the influence of IBL into the already described PBR system, let’s return to the familiar reflectivity equation: 3r31292. 3r? 31303.3r33333.3r3r1292. 3r? 31303. As previously described, the main goal is to calculate the integral for all incoming radiation directions 3r3-331203. 3r3903.over the hemisphere. In 3r31250. last lessonthe calculation of the integral was not burdensome, because we knew in advance the number of light sources, and, therefore, all those several directions of incidence of light corresponding to them. At the same time, the integral with a swoop does not solve: *

__any 3r31262. the falling vector3r3903.from the environment can carry with them a non-zero energy brightness. As a result, for the practical applicability of the method is required to meet the following requirements: 3r31292. 3r? 31303. 3r31277. 3r? 31303. 3r31284. It is necessary to come up with a way to get the energy brightness of the scene for an arbitrary direction vector 3r-31203. 3r3903.; 3r31287. 3r? 31303. 3r31284. It is necessary that the solution of the integral can occur in real time. 3r31287. 3r? 31303. 3r31289. 3r3r1292. 3r? 31303. 3r3r1292. 3r? 31303. Well, the first point is resolved by itself. Here, a hint of a solution has already passed: one of the methods for representing the irradiance of a scene or environment is a cubic map that has undergone special processing. Each texel in such a map can be considered as a separate radiating source. By sampling from such a map on an arbitrary vector 3r3-31203. 3r3903.we easily get the energy brightness of the scene in this direction. 3r3r1292. 3r? 31303. 3r3r1292. 3r? 31303. So, we get the energy brightness of the scene for an arbitrary vector3r3903.: 3r? 31303. 3r31234. 3r31119. vec3 radiance = texture (_cubemapEnvironment, w_i) .rgb; 3r31240. 3r31241. 3r3r1292. 3r? 31303. 3r3r1292. 3r? 31303. Remarkably, however, the solution of the integral requires us to take samples from the environment map not from one direction, but from all possible ones in the hemisphere. And so - for each shaded fragment. Obviously, for real-time tasks this is practically impracticable. A more effective method would be to calculate part of integrands in advance, still outside our application. But for this you have to roll up your sleeves and plunge deeper into the essence of the expression of reflectivity: 3r? 31303.3r33333.3r3r1292. 3r? 31303. It is seen that the parts of the expression associated with the scattered3r33393.and mirrorBRDF components are independent. You can divide the integral into two parts: 3r31292. 3r? 31303.3r33380.3r3r1292. 3r? 31303. Such a division into parts will allow us to deal with each of them separately, and in this lesson we will deal with the part responsible for the ambient lighting. 3r3r1292. 3r? 31303. 3r3r1292. 3r? 31303. After analyzing the form of the integral with respect to the diffuse component, we can conclude that the diffuse component of Lambert is essentially constant (3r33903. 3r31205., And 3r??? .3333333? 3r333339? 3r333339?does not depend on other variables. Taking this fact into account, one can take the constants behind the integral sign: 3r? 31303.3r33880.3r3r1292. 3r? 31303. So we get an integral that depends only on r3r31203. 3r3903.(it is assumed that 3r3–31203. 3r33470. 3r3–31205. corresponds to the center of the cubic environment map). Based on this formula, it is possible to calculate or, even better, pre-calculate a new cubic map that stores the result of calculating the integral of the diffuse component for each direction of the sample (or texel map) 3r-31203. using convolution operation. 3r3r1292. 3r? 31303. 3r3r1292. 3r? 31303. Convolution is the operation of applying some calculation to each element in the data set, taking into account the data of all the other elements of the set. In this case, such data is the energy brightness of the scene or the environment map. Thus, to calculate one value in each direction of the sample in a cubic map, we will have to take into account the values taken from all other possible directions of the sample on a hemisphere lying around the sample point. 3r3r1292. 3r? 31303. 3r3r1292. 3r? 31303. To convolve the environment map, we need to solve the integral for each resulting direction of the sample 3r-31203. by implementing multiple discrete samples along directions 3r3-31203. 3r3903.belonging to the hemisphere, and averaging the total energy brightness. The hemisphere on the basis of which the sample directions are taken is 3r3-31203. 3r3903.oriented along the vectorthat represents the target direction for which the convolution is currently being calculated. Look at the picture for a better understanding: 3r? 31303. 3r31254. 3r3444. 3r? 31304. 3r3r1292. 3r? 31303. 3r3r1292. 3r? 31303. Such a pre-calculated cubic map that stores the result of integration for each direction of the sample 3r-31203. , can also be considered as storing the result of summing up all indirect diffuse illumination in a scene falling on a surface oriented along thedirection. . In other words, such cubic maps are called irradiance maps, since a cubic environment map subjected to a preliminary convolution allows one to directly sample the magnitude of the scene irradiation coming from an arbitrary direction 3-3-31203. , without additional calculations. 3r3r1292. 3r? 31303. 3rr3461. The expression that determines the energy brightness also depends on the position of the sampling point 3r-31203. 3r33470.which we took lying in the center of the irradiance map. Such an assumption imposes a limitation in the sense that the source of all indirect diffuse illumination will also be the only environmental map. In scenes of different lighting, this can destroy the illusion of reality (especially in indoor scenes). Modern rendering engines solve this issue by placing special auxiliary objects in the scene - 3r-31206. samples of reflections 3r3-31207. (3r3-31206. Reflection probes 3r3-331207.). Each such object deals with one task: it forms its own irradiance map for its immediate environment. With such a technique, the irradiance (and energy brightness) at an arbitrary point3r33470.will be determined by simple interpolation between the nearest reflection samples. But for the current tasks, we agree that the selection of the environment map is conducted from its very center, and we shall analyze the reflection samples in further lessons.3r3r1292. 3r? 31303. Below is an example of a cubic environment map and an irradiance map obtained on its basis (by authorship 3r3-3475. Wave engine), Averaging the energetic brightness of the environment for each output direction. 3r3r1292. 3r? 31303. 3r31254. ), And outwardly such a card looks like it stores the average color of the environment map. A sample in any direction from such a map will return the value of irradiance coming from this direction. 3r3r1292. 3r? 31303. 3r3r1292. 3r? 31303. 3r31273. PBR and HDR3r3r1292. 3r? 31303. In 3r31250. the previous lessonthe fact that for corrections has already been briefly notedIn order for the PBR lighting model to work, it is extremely important to take into account the HDR brightness range of the light sources present. Since the PBR model at the input accepts parameters in one way or another based on quite specific physical quantities and characteristics, it is logical to require compliance of the energy brightness of light sources with their real prototypes. It does not matter how we justify a specific amount of radiation flux for each source: we make a rough engineering estimate or turn to 3r3502. physical quantities- the difference in performance between the room lamp and the sun will be huge in any case. Without using 3r3504. HDRrange, it will simply be impossible to accurately determine the relative brightness of various light sources. 3r3r1292. 3r? 31303. 3r3r1292. 3r? 31303. So PBR and HDR are friends forever, this is understandable, just how does this fact relate to image-based lighting methods? In the last lesson, it was shown that transferring PBR to the HDR rendering range is simple. One thing remains “but”: since the indirect illumination from the environment is based on a cubic environment map, a way is needed to preserve the HDR characteristics of this background lighting in the environment map. 3r3r1292. 3r? 31303. Until now, we used environment maps created in the LDR format (for example, Skyboxes ). We used a selection of colors from them in the rendering as is, and this is quite acceptable for direct object shading. And it is completely unsuitable when using environment maps as sources of physically reliable measurements. 3r3r1292. 3r? 31303. 3r3r1292. 3r? 31303. 3r33586. RGBE - image format in the HDR range 3r3353587. 3r3r1292. 3r? 31303. Get to know the RGBE image file format. Files with the extension “3r3-31206. .Hdr 3r3-31207.” Are used to store images with a wide dynamic range, allocating one byte for each element of the color triad and another byte for the total exponent. Including the format allows you to store and cubic environment maps with a range of color intensity beyond the[0., 1.]LDR range. . This means that light sources can retain their real intensity, being represented by such an environment map. 3r3r1292. 3r? 31303. The network has enough free environment maps in the RGBE format, taken in various real world conditions. Here, for example, an example from a site 3r3r2626. sIBL archive: 3r? 31303. 3r31254. 3r? 3531. 3r? 31304. 3r3r1292. 3r? 31303. 3r3r1292. 3r? 31303. You may be surprised at what you see: after all, this distorted image is not at all like an ordinary cubic map with its pronounced breakdown into 6 faces. The explanation is simple: this environment map was projected from a sphere onto a plane — 3r3-31206 was applied. equal-right scan__

__. This is done to allow storage in a format that does not support the storage mode of cubic cards as is. Of course, this projection method brings with it drawbacks: the horizontal resolution is much higher than the vertical. In most cases, the use in rendering is a valid ratio, since usually interesting details of the environment and lighting are located exactly in the horizontal plane, and not in the vertical. Well, plus to everything, we need the conversion code back to the cubic map. 3r3r1292. 3r? 31303. 3r3r1292. 3r? 31303. 3r33586. RGBE format support in stb_image.h__

3r3r1292. 3r? 31303. Downloading this image format on your own requires knowledge of 3r33547. specifications format 3r31297. that, albeit not difficult, but still time consuming. Fortunately for us, the image download library 3r33549. stb_image.h

implemented in a single header file, supports loading of RGBE files, returning an array of floating-point numbers - just what we need for our purposes! Having added a library to your project, downloading these images is implemented extremely simply:

3r? 31303. 3r31234. 3r31119. #include "stb_image.h"

[]3r? 31303. 3r? 31303. stbi_set_flip_vertically_on_load (true); 3r? 31303. int width, height, nrComponents; 3r? 31303. float * data = stbi_loadf ("newport_loft.hdr", & width, & height, & nrComponents, 0); 3r? 31303. unsigned int hdrTexture; 3r? 31303. if (data)

{

glGenTextures (? & hdrTexture); 3r? 31303. glBindTexture (GL_TEXTURE_2D, hdrTexture); 3r? 31303. glTexImage2D (GL_TEXTURE_2D, ? GL_RGB16F, width, height, ? GL_RGB, GL_FLOAT, data); 3r? 31303. 3r? 31303. glTexParameteri (GL_TEXTURE_2D, GL_TEXTURE_WRAP_S, GL_CLAMP_TO_EDGE); 3r? 31303. glTexParameteri (GL_TEXTURE_2D, GL_TEXTURE_WRAP_T, GL_CLAMP_TO_EDGE); 3r? 31303. glTexParameteri (GL_TEXTURE_2D, GL_TEXTURE_MIN_FILTER, GL_LINEAR); 3r? 31303. glTexParameteri (GL_TEXTURE_2D, GL_TEXTURE_MAG_FILTER, GL_LINEAR); 3r? 31303. 3r? 31303. stbi_image_free (data); 3r? 31303.}

else

{

std :: cout "Failed to load HDR image." std :: endl; 3r? 31303.} 3r31241. 3r3r1292. 3r? 31303. The library automatically converts the values from the internal HDR format to ordinary real 32-bit numbers, by default with three color channels. It is quite enough to save the data of the original HDR image in the usual 2D floating-point texture. 3r3r1292. 3r? 31303. 3r3r1292. 3r? 31303. 3r33586. Convert the equal-right scan of the image into a cubic map

3r3r1292. 3r? 31303. An even-right scan can be used for direct sampling from the environment map, but this would require expensive mathematical operations, while a sample from a normal cube map would be practically free of performance. It is for these reasons in this lesson that we will be engaged in converting an equal-rectangular image into a cubic map, which will be used later. However, the method of direct sampling from an equal-right map using a three-dimensional vector will also be shown here so that you can choose the method of work that is right for you. 3r3r1292. 3r? 31303. To convert, you need to draw a cube of a single size, watching it from the inside, project an equal-rectangular map on its face, and then extract six images from the faces as faces of a cube map. The vertex shader of this stage is quite simple: it simply processes the vertices of the cube as is, and also transfers their non-transformed positions to a fragmentary shader for use as a three-dimensional vector of the sample: 3r31292. 3r? 31303. 3r31234.

3r? 31303. 3r31234.

{

//note that the software uses 3r3-331303. //16-bit floating-point format

glTexImage2D (GL_TEXTURE_CUBE_MAP_POSITIVE_X + i, ? 3? 31_e, 39_31003. GL-TEXTURE_CUBE_MAP_POSITIVE_X + i, ? 39_31303. GLTEXTURE_CUBE_MAP_POSITIVE_X + i, ? 39_31303. GLTEXTURE_CUBE_MAP_POSITIVE_X + i, ? 3? 31_? 31_33031 .3 ? GL_RGB, GL_FLOAT, nullptr);

}

glTexParameteri (GL_TEXTURE_CUBE_MAP, GL_TEXTURE_WRAP_S, GL_CLAMP_TO_EDGE);.

glTexParameteri (GL_TEXTURE_CUBE_MAP, GL_TEXTURE_WRAP_T, GL_CLAMP_TO_EDGE);.

glTexParameteri (GL_TEXTURE_CUBE_MAP, GL_TEXTURE_WRAP_R, GL_CLAMP_TO_EDGE);.

glTexParameteri (GL_TEXTURE_CUBE_MAP , GL_TEXTURE_MIN_FILTER, GL_LINEAR); 3r3-330303. GlTexParameteri (GL_TEXTURE_CUBE_MAP, GL_TEXTURE_MAG_FILTER, GL_LINEAR); 3r? 31303. 3r3r1292. 3r? 31303. After this preparation, it will only be necessary to directly transfer parts of the equal-right map to the verge of the cube map. 3r3r1292. 3r? 31303. 3r3r1292. 3r? 31303. We will not go into much detail, especially since the code repeats in many ways what was seen in the lessons on frame buffer 3r31297. and 3r3705. Omnidirectional shadows . In principle, it all comes down to preparing six separate species matrices that orient the camera strictly to each of the faces of the cube, as well as a special projection matrix with a 90 ° angle of view to capture the entire face of the cube. Then, the rendering is simply carried out six times, and the result is saved to the floating-point framebuffer: 3r31292. 3r? 31303. 3r31234. 3r31119. glm :: mat4 captureProjection = glm :: perspective (glm :: radians (90.0f), 1.0f, 0.1f, 10.0f); 3r? 31303. glm :: mat4 captureViews[]=

{

glm :: lookAt (glm :: vec3 (0.0f, 0.0f, 0.0f), glm :: vec3 (1.0f, 0.0f, 0.0f), glm :: vec3 (0.0f, -1.0f, 0.0f) ), 3r33031. glm :: lookAt (glm :: vec3 (0.0f, 0.0f, 0.0f), glm :: vec3 (-1.0f, 0.0f, 0.0f), glm :: vec3 (0.0f, -1.0f, 0.0f )), 3r330313. glm :: lookAt (glm :: vec3 (0.0f, 0.0f, 0.0f), glm :: vec3 (0.0f, 1.0f, 0.0f), glm :: vec3 (0.0f, 0.0f, 1.0f)) ,

glm :: lookAt (glm :: vec3 (0.0f, 0.0f, 0.0f), glm :: vec3 (0.0f, -1.0f, 0.0f), glm :: vec3 (0.0f, 0.0f, -1.0f )), 3r330313. glm :: lookAt (glm :: vec3 (0.0f, 0.0f, 0.0f), glm :: vec3 (0.0f, 0.0f, 1.0f), glm :: vec3 (0.0f, -1.0f, 0.0f) ), 3r33031. glm :: lookAt (glm :: vec3 (0.0f, 0.0f, 0.0f), glm :: vec3 (0.0f, 0.0f, -1.0f), glm :: vec3 (0.0f, -1.0f, 0.0f )) 3r3-331303.}; 3r? 31303. 3r? 31303. //Translation of the HDR of the equal-right environment map into the equivalent cubic map 3r-31303. equirectangularToCubemapShader.use (); 3r? 31303. equirectangularToCubemapShader.setInt ("equirectangularMap", 0); 3r? 31303. equirectangularToCubemapShader.setMat4 ("projection", captureProjection); 3r? 31303. glActiveTexture (GL_TEXTURE0); 3r? 31303. glBindTexture (GL_TEXTURE_2D, hdrTexture); 3r? 31303. 3r? 31303. //do not forget to adjust the viewport parameters for correct capture

glViewport (? ? 51? 512); 3r? 31303. glBindFramebuffer (GL_FRAMEBUFFER, captureFBO); 3r? 31303. for (unsigned int i = 0; i < 6; ++i)

{

equirectangularToCubemapShader.setMat4 ( "view", captureViews

3r3r1292. 3r? 31303. Downloading this image format on your own requires knowledge of 3r33547. specifications format 3r31297. that, albeit not difficult, but still time consuming. Fortunately for us, the image download library 3r33549. stb_image.h

implemented in a single header file, supports loading of RGBE files, returning an array of floating-point numbers - just what we need for our purposes! Having added a library to your project, downloading these images is implemented extremely simply:

3r? 31303. 3r31234. 3r31119. #include "stb_image.h"

[]3r? 31303. 3r? 31303. stbi_set_flip_vertically_on_load (true); 3r? 31303. int width, height, nrComponents; 3r? 31303. float * data = stbi_loadf ("newport_loft.hdr", & width, & height, & nrComponents, 0); 3r? 31303. unsigned int hdrTexture; 3r? 31303. if (data)

{

glGenTextures (? & hdrTexture); 3r? 31303. glBindTexture (GL_TEXTURE_2D, hdrTexture); 3r? 31303. glTexImage2D (GL_TEXTURE_2D, ? GL_RGB16F, width, height, ? GL_RGB, GL_FLOAT, data); 3r? 31303. 3r? 31303. glTexParameteri (GL_TEXTURE_2D, GL_TEXTURE_WRAP_S, GL_CLAMP_TO_EDGE); 3r? 31303. glTexParameteri (GL_TEXTURE_2D, GL_TEXTURE_WRAP_T, GL_CLAMP_TO_EDGE); 3r? 31303. glTexParameteri (GL_TEXTURE_2D, GL_TEXTURE_MIN_FILTER, GL_LINEAR); 3r? 31303. glTexParameteri (GL_TEXTURE_2D, GL_TEXTURE_MAG_FILTER, GL_LINEAR); 3r? 31303. 3r? 31303. stbi_image_free (data); 3r? 31303.}

else

{

std :: cout "Failed to load HDR image." std :: endl; 3r? 31303.} 3r31241. 3r3r1292. 3r? 31303. The library automatically converts the values from the internal HDR format to ordinary real 32-bit numbers, by default with three color channels. It is quite enough to save the data of the original HDR image in the usual 2D floating-point texture. 3r3r1292. 3r? 31303. 3r3r1292. 3r? 31303. 3r33586. Convert the equal-right scan of the image into a cubic map

3r3r1292. 3r? 31303. An even-right scan can be used for direct sampling from the environment map, but this would require expensive mathematical operations, while a sample from a normal cube map would be practically free of performance. It is for these reasons in this lesson that we will be engaged in converting an equal-rectangular image into a cubic map, which will be used later. However, the method of direct sampling from an equal-right map using a three-dimensional vector will also be shown here so that you can choose the method of work that is right for you. 3r3r1292. 3r? 31303. To convert, you need to draw a cube of a single size, watching it from the inside, project an equal-rectangular map on its face, and then extract six images from the faces as faces of a cube map. The vertex shader of this stage is quite simple: it simply processes the vertices of the cube as is, and also transfers their non-transformed positions to a fragmentary shader for use as a three-dimensional vector of the sample: 3r31292. 3r? 31303. 3r31234.

` #version 330 core`

layout (location = 0) in vec3 aPos; 3r? 31303. 3r? 31303. out vec3 localPos; 3r? 31303. 3r? 31303. uniform mat4 projection; 3r? 31303. uniform mat4 view; 3r? 31303. 3r? 31303. void main ()

{

localPos = aPos; 3r? 31303. gl_Position = projection * view * vec4 (localPos, 1.0); 3r? 31303.}

3r31241. 3r3r1292. 3r? 31303. 3r3r1292. 3r? 31303. In the fragment shader, we shade each face of the cube as if we tried to carefully wrap the cube with a sheet with an equal-right card. To do this, the sampling direction transferred to the fragment shader is taken, processed by special trigonometric magic, and, ultimately, a sample is taken from the equal-right card as if it were actually a cube map. The result of the sample is directly saved as a fragment color of the face of the cube:3r? 31303. 3r31234.

` #version 330 core`

out vec4 FragColor; 3r? 31303. in vec3 localPos; 3r? 31303. 3r? 31303. uniform sampler2D equirectangularMap; 3r? 31303. 3r? 31303. const vec2 invAtan = vec2 (???? ???); 3r? 31303. vec2 SampleSphericalMap (vec3 v)

{

vec2 uv = vec2 (atan (v.z, v.x), asin (v.y)); 3r? 31303. uv * = invAtan; 3r? 31303. uv + = 0.5; 3r? 31303. return uv; 3r? 31303.}

3r? 31303. void main ()

{

//localPos requires normalization

vec2 uv = SampleSphericalMap (normalize (localPos)); 3r? 31303. vec3 color = texture (equirectangularMap, uv) .rgb; 3r? 31303. 3r? 31303. FragColor = vec4 (color, 1.0); 3r? 31303.}

3r31241. 3r3r1292. 3r? 31303. 3r3r1292. 3r? 31303. If you actually draw a cube with this shader and an associated HDR environment map, you get something like this: 3r31292. 3r? 31303. 3r31254. 3r? 31303. 3r31234. 3r31119. unsigned int captureFBO, captureRBO; 3r? 31303. glGenFramebuffers (? & captureFBO); 3r? 31303. glGenRenderbuffers (? & captureRBO); 3r? 31303. 3r? 31303. glBindFramebuffer (GL_FRAMEBUFFER, captureFBO); 3r? 31303. glBindRenderbuffer (GL_RENDERBUFFER, captureRBO); 3r? 31303. glRenderbufferStorage (GL_RENDERBUFFER, GL_DEPTH_COMPONENT2? 51? 512); 3r? 31303. glFramebufferRenderbuffer (GL_FRAMEBUFFER, GL_DEPTH_ATTACHMENT, GL_RENDERBUFFER, captureRBO); 3r31240. 3r31241. 3r3r1292. 3r? 31303. 3r3r1292. 3r? 31303. Of course, let's not forget to organize the memory for storing each of the six faces of the future cube map: 3r31292. 3r? 31303. 3r31234. 3r31119. unsigned int envCubemap; 3r? 31303. glGenTextures (? & envCubemap); 3r? 31303. glBindTexture (GL_TEXTURE_CUBE_MAP, envCubemap); 3r? 31303. for (unsigned int i = 0; i < 6; ++i){

//note that the software uses 3r3-331303. //16-bit floating-point format

glTexImage2D (GL_TEXTURE_CUBE_MAP_POSITIVE_X + i, ? 3? 31_e, 39_31003. GL-TEXTURE_CUBE_MAP_POSITIVE_X + i, ? 39_31303. GLTEXTURE_CUBE_MAP_POSITIVE_X + i, ? 39_31303. GLTEXTURE_CUBE_MAP_POSITIVE_X + i, ? 3? 31_? 31_33031 .3 ? GL_RGB, GL_FLOAT, nullptr);

}

glTexParameteri (GL_TEXTURE_CUBE_MAP, GL_TEXTURE_WRAP_S, GL_CLAMP_TO_EDGE);.

glTexParameteri (GL_TEXTURE_CUBE_MAP, GL_TEXTURE_WRAP_T, GL_CLAMP_TO_EDGE);.

glTexParameteri (GL_TEXTURE_CUBE_MAP, GL_TEXTURE_WRAP_R, GL_CLAMP_TO_EDGE);.

glTexParameteri (GL_TEXTURE_CUBE_MAP , GL_TEXTURE_MIN_FILTER, GL_LINEAR); 3r3-330303. GlTexParameteri (GL_TEXTURE_CUBE_MAP, GL_TEXTURE_MAG_FILTER, GL_LINEAR); 3r? 31303. 3r3r1292. 3r? 31303. After this preparation, it will only be necessary to directly transfer parts of the equal-right map to the verge of the cube map. 3r3r1292. 3r? 31303. 3r3r1292. 3r? 31303. We will not go into much detail, especially since the code repeats in many ways what was seen in the lessons on frame buffer 3r31297. and 3r3705. Omnidirectional shadows . In principle, it all comes down to preparing six separate species matrices that orient the camera strictly to each of the faces of the cube, as well as a special projection matrix with a 90 ° angle of view to capture the entire face of the cube. Then, the rendering is simply carried out six times, and the result is saved to the floating-point framebuffer: 3r31292. 3r? 31303. 3r31234. 3r31119. glm :: mat4 captureProjection = glm :: perspective (glm :: radians (90.0f), 1.0f, 0.1f, 10.0f); 3r? 31303. glm :: mat4 captureViews[]=

{

glm :: lookAt (glm :: vec3 (0.0f, 0.0f, 0.0f), glm :: vec3 (1.0f, 0.0f, 0.0f), glm :: vec3 (0.0f, -1.0f, 0.0f) ), 3r33031. glm :: lookAt (glm :: vec3 (0.0f, 0.0f, 0.0f), glm :: vec3 (-1.0f, 0.0f, 0.0f), glm :: vec3 (0.0f, -1.0f, 0.0f )), 3r330313. glm :: lookAt (glm :: vec3 (0.0f, 0.0f, 0.0f), glm :: vec3 (0.0f, 1.0f, 0.0f), glm :: vec3 (0.0f, 0.0f, 1.0f)) ,

glm :: lookAt (glm :: vec3 (0.0f, 0.0f, 0.0f), glm :: vec3 (0.0f, -1.0f, 0.0f), glm :: vec3 (0.0f, 0.0f, -1.0f )), 3r330313. glm :: lookAt (glm :: vec3 (0.0f, 0.0f, 0.0f), glm :: vec3 (0.0f, 0.0f, 1.0f), glm :: vec3 (0.0f, -1.0f, 0.0f) ), 3r33031. glm :: lookAt (glm :: vec3 (0.0f, 0.0f, 0.0f), glm :: vec3 (0.0f, 0.0f, -1.0f), glm :: vec3 (0.0f, -1.0f, 0.0f )) 3r3-331303.}; 3r? 31303. 3r? 31303. //Translation of the HDR of the equal-right environment map into the equivalent cubic map 3r-31303. equirectangularToCubemapShader.use (); 3r? 31303. equirectangularToCubemapShader.setInt ("equirectangularMap", 0); 3r? 31303. equirectangularToCubemapShader.setMat4 ("projection", captureProjection); 3r? 31303. glActiveTexture (GL_TEXTURE0); 3r? 31303. glBindTexture (GL_TEXTURE_2D, hdrTexture); 3r? 31303. 3r? 31303. //do not forget to adjust the viewport parameters for correct capture

glViewport (? ? 51? 512); 3r? 31303. glBindFramebuffer (GL_FRAMEBUFFER, captureFBO); 3r? 31303. for (unsigned int i = 0; i < 6; ++i)

{

equirectangularToCubemapShader.setMat4 ( "view", captureViews

*);*

glFramebufferTexture2D (GL_FRAMEBUFFER, GL_COLOR_ATTACHMENT?

GL_TEXTURE_CUBE_MAP_POSITIVE_X + i, envCubemap, 0);

glClear ( GL_COLOR_BUFFER_BIT | GL_DEPTH_BUFFER_BIT); 3r3-331303. 3r3-331303. RenderCube (); //output of a single cube 3r3-131303. 3r? 31303. 3r3r1292. 3r? 31303. It uses the attachment of the framebuffer color, and alternately changing the connected face of the cube map, which leads to the direct rendering of the render to one of the faces of the environment map. This code needs to be executed only once, after which we will have a full-fledged map of the environment

3r? 31303. 3r31234.glFramebufferTexture2D (GL_FRAMEBUFFER, GL_COLOR_ATTACHMENT?

GL_TEXTURE_CUBE_MAP_POSITIVE_X + i, envCubemap, 0);

glClear ( GL_COLOR_BUFFER_BIT | GL_DEPTH_BUFFER_BIT); 3r3-331303. 3r3-331303. RenderCube (); //output of a single cube 3r3-131303. 3r? 31303. 3r3r1292. 3r? 31303. It uses the attachment of the framebuffer color, and alternately changing the connected face of the cube map, which leads to the direct rendering of the render to one of the faces of the environment map. This code needs to be executed only once, after which we will have a full-fledged map of the environment

*in our hands. envCubemap*containing the result of the conversion of the original equal-right version of the HDR environment map. 3r3r1292. 3r? 31303. 3r3r1292. 3r? 31303. Test the resulting cubic map by sketching the simplest shader for skybox:3r? 31303. 3r31234.

` #version 330 core`

layout (location = 0) in vec3 aPos; 3r? 31303. 3r? 31303. uniform mat4 projection; 3r? 31303. uniform mat4 view; 3r? 31303. 3r? 31303. out vec3 localPos; 3r? 31303. 3r? 31303. void main ()

{

localPos = aPos; 3r? 31303. //here we discard the transfer data from the species matrix

mat4 rotView = mat4 (mat3 (view)); 3r? 31303. vec4 clipPos = projection * rotView * vec4 (localPos, 1.0); 3r? 31303. 3r? 31303. gl_Position = clipPos.xyww; 3r? 31303.}

3r31240. 3r31241. 3r3r1292. 3r? 31303. 3r3r1292. 3r? 31303. Note the trick with the components of the vector * clipPos * : we use the tetrad * xyww 3r3-31207. when recording the converted verticesto provide all skybox fragments with a maximum depth of 1.0 (the approach has already been used in 3r3785. relevant lesson ). Do not forget to change the comparison function to [i] GL_LEQUAL * :

3r? 31303. 3r31234. 3r31119. glDepthFunc (GL_LEQUAL); 3r31240. 3r31241. 3r3r1292. 3r? 31303. 3r3r1292. 3r? 31303. The fragment shader simply selects from a cubic map: 3r31292. 3r? 31303. 3r31234. ` version 330 core`

out vec4 FragColor; 3r? 31303. 3r? 31303. in vec3 localPos; 3r? 31303. 3r? 31303. uniform samplerCube environmentMap; 3r? 31303. 3r? 31303. void main ()

{

vec3 envColor = texture (environmentMap, localPos) .rgb; 3r? 31303. 3r? 31303. envColor = envColor /(envColor + vec3 (1.0)); 3r? 31303. envColor = pow (envColor, vec3 (1.0 /2.2)); 3r? 31303. 3r? 31303. FragColor = vec4 (envColor, 1.0); 3r? 31303.}

3r31241. 3r3r1292. 3r? 31303. 3r3r1292. 3r? 31303. The sample from the map is based on the interpolated local coordinates of the cube vertices, which is the correct direction of the sample in this case (again, discussed in the skybox lesson, 3-3-3?206. Lane. 3-3-3?207.). Since the transfer components in the view matrix were ignored, the skybox render will not depend on the observer's position, creating the illusion of an infinitely distant background. Since here we directly output data from the HDR card to the default framebuffer, which is an LDR receiver, it is necessary to recall tonal compression. And finally, almost all HDR maps are stored in linear space, which means that you need to apply 3r3826. gamma correction as a final chord processing. 3r3r1292. 3r? 31303. 3r3r1292. 3r? 31303. So, with the output of the received skybox, along with the already familiar array of spheres, we get something like this: 3r3r1292. 3r? 31303. 3r31254. . The code for the entire conversion process is here . 3r3r1292. 3r? 31303. 3r3r1292. 3r? 31303. 3r31273. Convolution of the cubic map 3r3r1292. 3r? 31303. As stated at the beginning of the lesson, our main goal is to solve the integral for all possible directions of indirect diffuse illumination, taking into account the given irradiance of the scene in the form of a cubic map of the environment. It is known that we can get the energy brightness value of the scene 3r3-31203. 3r33854. for arbitrary direction 3r3903. by sampling from HDR of a cubic environment map in this direction. To solve the integral, it will be necessary to sample the energy brightness of the scene from all possible directions in the hemisphere 3r-31203. each considered fragment. 3r3r1292. 3r? 31303. Obviously, the task of sampling the lighting from the environment from all possible directions in the hemisphere of 3r-31203. is computationally impossible - there are an infinite number of such directions. However, it is possible to apply the approximation by taking a finite number of directions chosen randomly or evenly spaced inside the hemisphere. This will make it possible to obtain a fairly good approximation to the true irradiance, in effect solving the integral of interest to us in the form of a finite sum. 3r3r1292. 3r? 31303. But for real-time tasks, even this approach is still incredibly superimposed, because the samples are made for each fragment, and the number of samples must be high enough for an acceptable result. Thus, it would be nice * prepare in advance * The data for this step is outside the rendering process. Since the orientation of the hemisphere determines from which region of space we imprint the irradiance, it is possible to calculate in advance the irradiance for each possible orientation of the hemisphere on the basis of all possible outgoing directions 3r31203. :

3r? 31303.

` `

` `

` 3r33880. `

` 3r3r1292. 3r? 31303. As a result, for a given arbitrary vector 3r3903. we will be able to sample from a pre-calculated irradiance map in order to obtain a diffuse irradiance value in this direction. To determine the amount of indirect diffuse radiation at the point of the current fragment, we take the total irradiance from the hemisphere oriented along the normal to the fragment surface. In other words, getting the irradiance of a scene comes down to a simple sample:`

3r? 31303. 3r31234. ` vec3 irradiance = texture (irradianceMap, N); 3r? 31303. 3r31240. 3r31241. 3r3r1292. 3r? 31303. 3r3r1292. 3r? 31303. Further, to create an irradiance map, it is necessary to perform a convolution of the environment map converted to a cubic map. We know that for each fragment its hemisphere is considered to be oriented along the normal to the surface 3r-31203. . In this case, the convolution of the cubic map is reduced to the calculation of the averaged sum of the energy brightness from all directions 3–3–31203. 3r3903. inside the hemisphere oriented along the normal :`

3r? 31303. 3r31254. 3r33914. 3r? 31304. 3r3r1292. 3r? 31303. 3r3r1292. 3r? 31303. Fortunately, the time-consuming preliminary work that we did at the beginning of the lesson will now allow you to quite simply convert the environment map as a cubic card in a special fragment shader, the output of which will be used to form a new cubic map. For this, the same piece of code that was used to translate the equal-right environment map into a cubic map comes in handy. It only remains to take another processing shader: 3r31292. 3r? 31303. 3r31234. ` #version 330 core`

out vec4 FragColor; 3r? 31303. in vec3 localPos; 3r? 31303. 3r? 31303. uniform samplerCube environmentMap; 3r? 31303. 3r? 31303. const float PI = ???; 3r? 31303. 3r? 31303. void main ()

{

//the direction of sampling is identical to the direction of orientation of the hemisphere 3r3-331303. vec3 normal = normalize (localPos); 3r? 31303. 3r? 31303. vec3 irradiance = vec3 (0.0); 3r? 31303. 3r? 31303.[]//convolution code

3r? 31303. FragColor = vec4 (irradiance, 1.0); 3r? 31303.}

3r31241. 3r3r1292. 3r? 31303. 3r3r1292. 3r? 31303. Here is the sampler * environmentmap * represents the HDR cubic map of the environment, previously obtained from the equal-right angle. 3r3r1292. 3r? 31303. 3r3r1292. 3r? 31303. There are many ways to perform a convolution of the environment map; in this case, for each texel of a cubic map, we will create several sample vectors from the hemisphere of 3r-31203. oriented along the sample direction and average results. The number of vectors of the sample will be fixed, and the vectors themselves are evenly distributed inside the hemisphere. I note that the integrand is a continuous function, and the discrete estimate of this function will be only an approximation. And the more sample vectors we take, the closer we will be to the analytical solution of the integral. 3r3r1292. 3r? 31303. The integrand of the expression for reflectivity depends on the solid angle 3r-31203. 3r3393963. - values with which it is not very convenient to work. Instead of integrating over the solid angle 3r3393963. we change the expression, leading to integration by spherical coordinates 3r3-31203. 3r3-1023. and 3r33939. :

3r? 31303. 3r31254. 3r33981. . Angle 3r3-1023. will represent the elevation angle, varying from 0 to 3r33987. . The modified expression for reflectivity in such terms is as follows:

3r? 31303.

` `

` `

` 3r3995. `

` 3r3r1292. 3r? 31303. The solution of such an integral will require taking a finite number of samples in the hemisphere of 3r-31203. and averaging the results. Knowing the number of samples and for each of the spherical coordinates, one can translate the integral to 3r3-31009. The Riemannian sum :`

3r? 31303.

` `

` `

` `

` 3r3r1292. 3r? 31303. Since both spherical coordinates change discretely, at each moment the sample is taken from a certain averaged area over the hemisphere, as can be seen in the figure above. Due to the nature of the spherical surface, the size of the area of a discrete sample inevitably decreases with an increase in the elevation angle of 3r-31203. 3r3-1023. and approaching the zenith. To compensate for this effect of reducing the area, we added a weighting factor of 3r3–31203 to the expression. 3r31026. . 3r3r1292. 3r? 31303. 3r3r1292. 3r? 31303. As a result, the implementation of discrete sampling in a hemisphere based on spherical coordinates for each fragment in the form of a code looks like this: 3r31292. 3r? 31303. 3r31234. `` vec3 irradiance = vec3 (0.0); 3r? 31303. 3r? 31303. vec3 up = vec3 (0.? 1.? 0.0); 3r? 31303. vec3 right = cross (up, normal); 3r? 31303. up = cross (normal, right); 3r? 31303. 3r? 31303. float sampleDelta = ???; 3r? 31303. float nrSamples = 0.0; 3r? 31303. for (float phi = 0.0; phi < 2.0 * PI; phi += sampleDelta)`

{3r3-331303. for (float theta = 0.0; theta < 0.5 * PI; theta += sampleDelta)

{3r3-331303. //translation of spherical coordinates to Cartesian (in tangent pr-ve)

vec3 tangentSample = ve???.3 .31 tangentSample = 0.3 theta) * cos (phi), sin (theta) * sin (phi), cos (theta));

//from the tangent to world space

vec3 sampleVec = tangentSample.x * right + tangentSample.y * up + tangentSample.z * N; 3r3-331303. 3r3-331303. irradiance + = texture (environmentMap, sampleVec) .rgb * cos (theta) * sin (theta); 3r3-331303. nrSamples ++; 3r330303.} 3r33031303 .3033031303. (1.0 /float (nrSamples)); 3r33031.

3r? 31303. 3r3r1292. 3r? 31303. The variable is * sampleDelta * determines the size of the discrete step on the surface of the hemisphere. By changing this value, you can increase or decrease the accuracy of the result. 3r3r1292. 3r? 31303. Inside both cycles, the usual 3-dimensional vector of the sample is formed from spherical coordinates, transferred from the tangent to world space, and then used to select the cubic environment map from HDR. The result of the samples is accumulated in the variable * irradiance * which in the final processing will be divided by the number of samples taken in order to obtain the average value of irradiance. Note that the result of sampling from a texture is modulated by two values: * cos (theta) * - to account for the attenuation of light at large angles, and * sin (theta) * - to compensate for the reduction of the sample area when approaching the zenith. 3r3r1292. 3r? 31303. It remains only to deal with the code that renders and captures the results of the convolution of the environment map 3r-31206. envCubemap

` . First, create a cubic map to store the irradiance (you will need to perform it once, before entering the main render cycle): 3r31292. 3r? 31303. 3r31234. 3r31119. unsigned int irradianceMap; 3r? 31303. glGenTextures (? & irradianceMap); 3r? 31303. glBindTexture (GL_TEXTURE_CUBE_MAP, irradianceMap); 3r? 31303. for (unsigned int i = 0; i < 6; ++i)`

{

glTexImage2D (GL_TEXTURE_CUBE_MAP_POSITIVE_X + i, ? GL_RGB16F, 3? 3? ?

GL_RGB, GL_FLOAT, nullptr);

}.

glTexParameteri (GL_TEXTURE_CUBE_MAP, GL_TEXTURE_WRAP_S,. GL_CLAMP_TO_EDGE);.

glTexParameteri (GL_TEXTURE_CUBE_MAP, GL_TEXTURE_WRAP_T, GL_CLAMP_TO_EDGE);.

glTexParameteri (GL_TEXTURE_CUBE_MAP, GL_TEXTURE_WRAP_R, GL_CLAMP_TO_EDGE);.

glTexParameteri (GL_TEXTURE_CUBE_MAP, GL_TEXTURE_MIN_FILTER, GL_LINEAR);.

glTexParameteri (GL_TEXTURE_CUBE_MAP, GL_TEXTURE_MAG_FILTER, GL_LINEAR);.

3r? 31303. 3r3r1292. 3r? 31303. Since the irradiance map is obtained on the basis of averaging evenly distributed samples of the energy brightness of the environment map, it almost does not contain high-frequency parts and elements — a rather small resolution texture (here 32x32) and linear filtering will be enough to store it. 3r3r1292. 3r? 31303. Next, configure the capture framebuffer for this resolution:

3r? 31303. 3r31234. 3r31119. glBindFramebuffer (GL_FRAMEBUFFER, captureFBO); 3r? 31303. glBindRenderbuffer (GL_RENDERBUFFER, captureRBO); 3r? 31303. glRenderbufferStorage (GL_RENDERBUFFER, GL_DEPTH_COMPONENT2? 3? 32); 3r? 31303. 3r31240. 3r31241. 3r3r1292. 3r? 31303. 3r3r1292. 3r? 31303. The code for capturing the results of a convolution is similar to the code for translating an environment map from equilateral to cubic, only the convolution shader is used: 3r31292. 3r? 31303. 3r31234. 3r31119. irradianceShader.use (); 3r? 31303. irradianceShader.setInt ("environmentMap", 0); 3r? 31303. irradianceShader.setMat4 ("projection", captureProjection); 3r? 31303. glActiveTexture (GL_TEXTURE0); 3r? 31303. glBindTexture (GL_TEXTURE_CUBE_MAP, envCubemap); 3r? 31303. 3r? 31303. //do not forget to adjust the viewport to the captured size

glViewport (? ? 3? 32); 3r? 31303. glBindFramebuffer (GL_FRAMEBUFFER, captureFBO); 3r? 31303. for (unsigned int i = 0; i < 6; ++i)

{

irradianceShader.setMat4 ( "view", captureViews*);*

glFramebufferTexture2D (GL_FRAMEBUFFER, GL_COLOR_ATTACHMENT?

GL_TEXTURE_CUBE_MAP_POSITIVE_X + i, irradianceMap, 0);

glClear ( GL_COLOR_BUFFER_BIT | GL_DEPTH_BUFFER_BIT); 3r3-???-331303. RenderCube (); 3r3-331303.} 3r3-331303. GlBindFramebuffer (GL_FRAMEBUFFER, 0), 3r3r???.???.???.???.???.???.3????.???.???.???.???.???.???.???.??? 3r? 31303. 3r3r1292. 3r? 31303. After completing this step, we will have a pre-calculated irradiance map on our hands, which can be directly used to calculate indirect diffuse illumination. To check how the convolution took place, try replacing the skybox texture from the environment map with the irradiance map:

3r? 31303. 3r31254. 3r31148. 3r? 31304. 3r3r1292. 3r? 31303. 3r3r1292. 3r? 31303. If as a result you saw something resembling a strongly blurred map of the environment, then, most likely, the convolution was successful. 3r3r1292. 3r? 31303. 3r3r1292. 3r? 31303. 3r31273. PBR and indirect radiation 3r31274. 3r3r1292. 3r? 31303. The resulting irradiance map is used in the diffuse part of the divided expression of reflectivity and represents the accumulated contribution from all possible directions of indirect illumination. Since in this case the light does not come from specific sources, but from the environment as a whole, we consider diffuse and specular indirect illumination as background (3r31206. Ambient 3r3-331207.), Replacing the previously used constant value. 3r3r1292. 3r? 31303. For a start, let's not forget to add a new sampler with an irradiance map: 3r31292. 3r? 31303. 3r31234. ` uniform samplerCube irradianceMap; 3r31240. 3r31241. 3r3r1292. 3r? 31303. 3r3r1292. 3r? 31303. Having an irradiance map that stores all the information about the indirect diffuse radiation of a scene, and the normal to the surface, it’s as easy to get data about the irradiance of a particular fragment as to make one sample from the texture: 3r31292. 3r? 31303. 3r31234. `` //vec3 ambient = vec3 (???); 3r? 31303. vec3 ambient = texture (irradianceMap, N) .rgb; 3r? 31303. 3r31240. 3r31241. 3r3r1292. 3r? 31303. 3r3r1292. 3r? 31303. However, since indirect radiation contains data for both the diffuse and specular components (as we saw in the component-separated version of the reflectivity expression), we will need to modulate the diffuse component in a special way. Just as in the previous lesson, we use the Fresnel expression to determine the degree of reflection of light for a given surface, from which we obtain the degree of refraction of light or the diffuse coefficient:`

3r? 31303. 3r31234. ` vec3 kS = fresnelSchlick (max (dot (N, V), 0.0), F0); 3r? 31303. vec3 kD = 1.0 - kS; 3r? 31303. vec3 irradiance = texture (irradianceMap, N) .rgb; 3r? 31303. vec3 diffuse = irradiance * albedo; 3r? 31303. vec3 ambient = (kD * diffuse) * ao; 3r? 31303. 3r31240. 3r31241. 3r3r1292. 3r? 31303. 3r3r1292. 3r? 31303. Because background lighting falls from all directions in the hemisphere based on the normal to the surface 3r-31203. then it is impossible to determine a single median ( [i] halfway `

` ) vector to calculate the fresnel coefficient. In order to imitate the Fresnel effect in such conditions, it is necessary to calculate the coefficient based on the angle between the normal and the observation vector. However, earlier, as a parameter, we used the median vector obtained from the microsurface model and depending on the surface roughness as a parameter for calculating the Fresnel coefficient. Since in this case the roughness is not included in the calculation parameters, the degree of reflection of light by the surface will always be overestimated. Indirect lighting as a whole should behave in the same way as direct lighting, i.e. from rough surfaces, we expect a lower degree of reflection at the edges. But since the roughness is not taken into account, the degree of mirror reflection according to Fresnel for indirect illumination looks unrealistic on rough non-metallic surfaces (in the image below, the described effect is exaggerated for greater clarity): 3r31292. 3r? 31303. 3r31254. 3r31211. 3r? 31304. 3r3r1292. 3r? 31303. 3r3r1292. 3r? 31303. To get around this trouble, you can add roughness to the Fremen-Schlick expression, the process described in 3r31217. Sébastien Lagarde :`

3r? 31303. 3r31234. ` vec3 fresnelSchlickRoughness (float cosTheta, vec3 F? float roughness)`

{

return F0 + (max (vec3 (1.0 - roughness), F0) - F0) * pow (1.0 - cosTheta, 5.0); 3r? 31303.}

3r31241. 3r3r1292. 3r? 31303. 3r3r1292. 3r? 31303. Taking into account the surface roughness in calculating the Fresnel kit, the code for calculating the background component takes the following form: 3r31292. 3r? 31303. 3r31234. ` vec3 kS = fresnelSchlickRoughness (max (dot (N, V), 0.0), F? roughness); 3r? 31303. vec3 kD = 1.0 - kS; 3r? 31303. vec3 irradiance = texture (irradianceMap, N) .rgb; 3r? 31303. vec3 diffuse = irradiance * albedo; 3r? 31303. vec3 ambient = (kD * diffuse) * ao; 3r31240. 3r31241. 3r3r1292. 3r? 31303. 3r3r1292. 3r? 31303. As it turned out, the use of illumination based on an image is inherently reduced to a single sample from a cube map. All the difficulties are mainly related to the preliminary preparation and transfer of the environment map to the irradiance map. 3r3r1292. 3r? 31303. 3r3r1292. 3r? 31303. Taking a familiar scene from a lesson on analytical sources 3r31297. light, containing an array of spheres with changing metallicity and roughness, and adding a diffuse background lighting from the environment, you get something similar: 3r3r1292. 3r? 31303. 3r31254. 3r31255. 3r? 31304. 3r3r1292. 3r? 31303. 3r3r1292. 3r? 31303. It still looks strange, since materials with a high degree of metallicity are still 3r3-31261. require `

` the presence of reflection in order to truly look, hmm, metal (metals do not reflect diffuse lighting). And in this case, the only reflections obtained from point analytical sources of light. And yet, we can already say that the spheres look more immersed in the environment (especially noticeable when switching environment maps), since the surfaces now correctly respond to the background lighting from the surroundings of the scene. 3r3r1292. 3r? 31303. 3r3r1292. 3r? 31303. The complete source code for the lesson is`

here . In the next lesson we will finally deal with the second half of the expression of reflectivity, which is responsible for indirect mirror lighting. After this step, you will truly feel the power of the PBR approach to lighting. 3r3r1292. 3r? 31303. 3r3r1292. 3r? 31303. 3r31273. Additional materials 3r31274. 3r3r1292. 3r? 31303. 3r31277. 3r? 31303. 3r31284. 3r31280. Coding Labs: Physically based rendering

: an introduction to the PBR model along with an explanation of how the irradiance map is constructed and why it is needed. 3r31287. 3r? 31303. 3r31284. 3r31285. The Mathematics of Shading

: ScratchAPixel's brief overview of some of the mathematical techniques used in this lesson, in particular about polar coordinates and integrals. 3r31287. 3r? 31303. 3r31289. 3r3r1292. 3r? 31303. 3r3r1292. 3r? 31303. 3r31294. P.S. 3r31295. A: We have telegram-konfa to coordinate transfers. If there is a serious desire to help with the translation, then you are welcome! 3r? 31304. 3r? 31303. 3r? 31303.

! function (e) {function t (t, n) {if (! (n in e)) {for (var r, a = e.document, i = a.scripts, o = i.length; o-- ;) if (-1! == i[o].src.indexOf (t)) {r = i[o]; break} if (! r) {r = a.createElement ("script"), r.type = "text /jаvascript", r.async =! ? r.defer =! ? r.src = t, r.charset = "UTF-8"; var d = function () {var e = a.getElementsByTagName ("script")[0]; e.parentNode.insertBefore (r, e)}; "[object Opera]" == e.opera? a.addEventListener? a.addEventListener ("DOMContentLoaded", d,! 1): e.attachEvent ("onload", d ): d ()}}} t ("//mediator.mail.ru/script/2820404/"""_mediator") () (); 3r? 31302. 3r? 31303. 3r? 31304.

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